Minutes after President Barack Obama said that the U.S. has held "high level" discussions with Russia about NSA leaker Edward Snowden's extradition, Russian President Vladimir Putin said Russia would "never" hand him over.

Reuters reports that Putin also said that if Snowden wants to stay in Russia, he must "stop his work aimed at harming our American partners" in leaking secret information about the National Security Agency's surveillance programs.

"There is one condition if he wants to remain here: He must stop his work aimed at damaging our American partners. As odd as it may sound from me," Putin said at a press conference.

It's unclear what other countries are on that list, but Snowden's appeal came one day after Ecuador President Rafael Correa backed away from suggestions that his country would provide Snowden with asylum.